**Heat Pipe and Phase Change Heat Transfer Technologies for Electronics Cooling**

Chan Byon

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62328

#### **Abstract**

The heat pipe is a well-known cooling module for advanced electronic devices. The heat pipe has many applications, particularly in electronics and related area such as PC, laptop, display, artificial satellite, and telecommunication modules. The heat pipe utilizes phase change heat transfer inside enveloped structures, where the working fluid evaporates in heated zone, and vapor moves to the condenser, and the condensed liquid is pumped back through microporous structure call wick. The performance of applicability in electronics of heat pipe is strongly dependent on the geometry, working fluid, and microstructure of wick. Therefore, it is worth considering the theory and technologies related to heat pipes for advanced electronics cooling. According to the purpose of this chapter mentioned above, the author considers fundamental aspects regarding heat pipe and phase change phenomena. First, the working principle of heat pipe is introduced. Important parameters in heat pipe are considered, and theoretical model for predicting the thermal performance of the heat pipe is introduced. In addition, design method for heat pipe is presented. Finally, applications of heat pipe to electronics cooling are presented. This chapter covers knowledge and state-of-art technologies in regard to heat pipe and phase change heat transfer. For a reliable operation of future electronics that have ultra-high heat flux amounts to 1000 W/m2 , heat pipe and phase change heat transfer are essential. This chapter provides the most valuable opportuni‐ ty for all readers from industry and academia to share the professional knowledge and to promote their ability in practical applications.

**Keywords:** Heat pipe, phase change, wick, design, analysis

## **1. Introduction**

Effective cooling technology is a crucial requirement for a reliable operation of electronic components. The electronics cooling methods can be hierarchically classified as chip level

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

cooling, package level cooling, and system level cooling, depending on the geometrical scale. In the package or system level cooling, the cooling modules such as heat sinks and heat pipes are widely employed for an efficient dissipation of heat as well as uniform temperature distribution. Especially, the use of heat pipes for electronics cooling has recently been increas‐ ing abruptly because the heat pipe is an attractive passive cooling scheme, which can offer high effective thermal conductivity and large heat transport capability. As shown in **Figure 1**, the heat pipes have been conventionally used for PCs, laptops, telecommunication units, solar collectors, small energy systems such as geothermal pipes, and satellites. Recently, the appli‐ cation of heat pipe even includes smart phones, vehicle headlight, gas burner, LED products, and agricultural systems, as shown in **Figure 2**.

**Figure 1.** Heat pipe applications.

The heat pipe is a thermal superconductor of which thermal conductivity amounts to several thousands of Watts per meter-Kelvin. Due to the extremely high effective thermal conductiv‐ ity, the heat pipe can handle a large amount of heat transfer with a negligible temperature drop. In addition, the heat pipe is a passive cooling module, which accompanies no power consumption or moving parts. Literally, the heat pipe is apparently just a pipe without any accessories for operating it. Furthermore, the shape of the heat pipe does not necessarily have to be cylindrical, but it can be formed into various shapes such as disks, flat plates, and airfoils. Attributable to these characteristics, the heat pipe is regarded as an ultimate candidate for addressing the thermal problem of concurrent high-power-density semiconductor industry, which encompasses solar cell, LEDs, power amplifiers, lasers, as well as electronic devices.

**Figure 2.** Recent applications.

**Figure 3.** The superiority of heat pipe over other thermally conducting materials.

**Figure 3** clearly illustrates the superiority of the heat pipe. The goodness of the heat transfer module is characterized by the effective thermal conductivity (*k*eff) or thermal resistance (*R*th) of the module. As an example, a typical value of effective thermal conductivity of a copper– water heat pipe with 0.5-m length and 1/2 inch diameter is around 10,000 W/mK, which is much larger than those of thermally conductive metals such as copper (~377 W/mK) or aluminum (~169 W/mK). This results in very low thermal resistance (~0.3 K/W), indicating low temperature drop with respect to the given thermal load. When 20 W heat is applied, this heat pipe would yield 6°C temperature difference between heat source and sink, whereas metal rods with same geometry have 206°C and 460°C for copper and aluminum, respectively. Provided that the ambient air is at 20°C, the chip temperature is only 26°C, which enables designers to easily come up with plausible and fascinating thermal solution.

In this chapter, general aspects of heat pipes for electronics cooling are introduced. The contents cover the working principle of heat pipes, design and analyzation methods, compo‐ nents and structure of heat pipes, implementation in electronics cooling, characterization and theories, and design and manufacturing process.

## **2. Working principle**

#### **2.1. Introduction to working principle**

The working principle of the heat pipe is summarized in **Figure 4**. The heat pipe consists of metal envelope, wick, and working fluid. The wick is a microporous structure made of metal and is attached to the inner surface of the envelope. The working fluid is located in the void space inside the wick. When the heat is applied at the evaporator by an external heat source, the applied heat vaporizes the working fluid in the heat pipe. The generated vapor of working fluid elevates the pressure and results in pressure difference along the axial direction. The pressure difference drives the vapor from evaporator to the condenser, where it condenses releasing the latent heat of vaporization to the heat sink. In the meantime, depletion of liquid by evaporation at the evaporator causes the liquid–vapor interface to enter into the wick surface, and thus a capillary pressure is developed there. This capillary pressure pumps the condensed liquid back to the evaporator for re-evaporation of working fluid. Likewise, the working fluid circulates in a closed loop inside the envelope, while evaporation and conden‐ sation simultaneously take place for heat absorption and dissipation, respectively. The high thermal performance of the heat pipe is originated from the latent heat of vaporization, which typically amounts to millions of Joules per 1 kg of fluid.

**Figure 4.** Working principle of heat pipe.

#### **2.2. Wick for heat pipe**

The flow in the wick is attributable to the same mechanism with the suction of water by a sponge. The microsized pores in the sponge (or wick) can properly generate the meniscus at the liquid–vapor interfaces, and this yields the capillary pressure gradient and resulting liquid movement. It should be noted that the wick provides the capillary pumping of working fluid, which must be steadily supplied for the operation of heat pipe as well as the flow passage of the working fluid. In addition, the wick also acts as a thermal flow path because the applied heat is transferred to the working fluid through the envelope and wick. Therefore, the thermal performance of the heat pipe is strongly dependent on the wick structure.

**Figure 5.** Typical wick structures.

In this regard, various types of wick structures have been used for enhancing the thermal performance of heat pipes. **Figure 5** shows three representative types of wick structures: mesh screen wick (it is also often termed as fiber mesh or wrapped screen), grooved wick, and sintered particle (or sintered powder) wick. The mesh screen wick is the most common wick structure, which made of wrapped textiles of metal wires. The grooved wick utilizes axial grooves directly sculptured on the envelope inner surface as the flow channel. The sintered particle wick is made of slightly fusing microsized metal particles together in the sintering process. The major characteristics of aforementioned wick types are shown in **Figure 6**. The mesh screen wick can have high capillary pressure and moderate permeability because numerous pores per unit length and the tightness of the structure can be controlled, where the permeability is a measure of the ability of a porous medium to transmit fluids through itself under a given pressure drop as follows:


$$dU = -\frac{K}{\mu} \frac{dP}{dx} \tag{1}$$

**Figure 6.** Characteristics of wick structures.

where *K* is the permeability, *U* is the mean velocity of flow inside porous media, *μ* is the viscosity, and d*P*/d*x* is the applied pressure gradient.

However, the effective thermal conductivity is low because the screens are not thermally connected to each other. In case of grooved wick, the effective thermal conductivity is high due to the sturdy thermal path. It has an additional advantage in which the wide and straight (not tortuous) flow path can bring about high permeability. However, the capillary pressure is strongly limited, due to the fact that the scale of the grooves, which are machined through extrusion process, cannot be reduced beyond several tens of micrometers. It should be noted that the maximum developable capillary pressure is inversely proportional to the characteristic length of the pore structure. On the other hand, the sintered particle wick has high capillary pressure as well as moderate-to-high effective thermal conductivity, due to the tailorable particle size and fused contact between particles. However, the permeability of the sintered particle wick is relatively low, due to the narrow and tortuous flow path. As shown, the type of wick has its pros and cons. Therefore, the designers choose the wick type in accordance with the corresponding suitable applications.

## **3. Thermal performance**

#### **3.1. Various mechanisms**

**Figure 7.** Performance limitations with respect to the temperature.

In case of other cooling modules, there is no heat transfer 'limitation,' implying that increasing heat transfer rate just keeps increasing the temperature drop and worsening the situation. On the contrary, there is a definite limitation of thermal performance for heat pipe, beyond which the heat transfer rate cannot be increased for a reliable operation. The thermal performance of the heat pipe is limited by one of various mechanisms depending on the working temperature range and geometry of the heat pipe. The viscous limit typically occurs during unsteady startup at low temperature, when the internal pressure drop is not large enough to move the vapor along the heat pipe. The sonic limit also typically takes place during unsteady start-up at low temperature, when the chocked flow regime is reached at the sonic speed of the vapor. The capillary limit is related to the ability of the wick to move the liquid through the required pressure drop. It happens when the circulation rate of working fluid increases so that the pressure drop along the entire flow path reaches the developed capillary pressure. When the capillary limit happens, dry out occurs in the evaporator, while more fluid is vaporized than that can be supplied by the capillary action of the wick. The entrainment limit is related to the liquid–vapor interface where counterflows of two phases are met. In some circumstances, the drag imposed by the vapor on the returning liquid can be large enough to entrain the flow of condensate in the wick structures, resulting in dry out. The boiling limit is known to occur when the bubble nucleation is initiated in the evaporator section. The bubble generally cannot easily escape the wick with microsized pores and effectively prevent the liquid to wet the heated surface, which in turn results in burnout. The burnout heat flux is known to typically range from 20 to 30 W/cm2 for sintered particle wicks.

**Figure 8.** Capillary limit and boiling limit.

**Figure 7** shows the thermal capacity of a heat pipe (copper–water, 1 cm diameter, 30 cm long) determined by various limiting mechanisms with respect to temperature. As shown in this figure, the viscous limit, the sonic limit, and the entrainment limit do not play an important role in determining the thermal capacity of the heat pipe, unless the temperature is very low (< −20°C). The heat pipes operating above atmospheric temperature are practically only governed by the capillary limit or the boiling limit, as shown in **Figure 7**. There is a good method for distinguishing those two limitations (see **Figure 8**). The capillary limit occurs when the liquid flow along the axial direction cannot afford the evaporation rate due to the limited capillary pressure. The boiling limit occurs when the bubble barricades the liquid flow onto the heated surface. In other words, the capillary limit is represented by the axial (or lateral) fluid transportation limit while the boiling limit is represented by the radial (or vertical) fluid transportation limit. It should be noted that, in the heat pipe, the limitation on the fluid transport represents the heat transfer limit because the heat transfer rate is given as the multiplication of latent heat coefficient and mass flow rate of working fluid. In this regard, the boiling limit becomes dominant when the effective heat pipe length is relatively small, and vice versa. The boiling limit also becomes important when the operating temperature is high because bubble nucleation is more likely to happen in high superheat. The next two subsections will be devoted to the models for capillary limit and boiling limit, respectively.

#### **3.2. Capillary limit**

The capillary limit is also called the wicking limit. As mentioned, the capillary limit occurs when the liquid flow along the axial direction cannot afford the evaporation rate. This situation happens under the condition where the pressure drop along the entire flow path is equal to the developed capillary pressure. The pressure drop of working fluid consists of that of liquid flow path (Δ*Pl* ), that of vapor flow path (Δ*Pv*), additional pressure drop imposed by counter‐ flow at the phase interface (Δ*Pl*–*<sup>v</sup>*), and the gravitational pressure drop (Δ*Pg*). Thus, the condition for the capillary limit is described by the following equation:

$$
\Delta P\_{\varepsilon} = \Delta P\_l + \Delta P\_{l-\nu} + \Delta P\_{\nu} + \Delta P\_g \tag{2}
$$

where Δ*Pc* is the capillary pressure difference between evaporator and condenser sections. Generally, the vapor pressure drop (Δ*Pv*) and interfacial pressure drop (Δ*Pl–v*) are negligible when compared with others; thus, the equation reduces to the following:

$$\frac{2\sigma}{R\_{\text{eff}}} = \frac{\mu\_l L\_{\text{eff}}}{K A\_w \rho\_l} \dot{m} + \rho\_l \text{g} L\_{\text{eff}} \sin \phi \tag{3}$$

where the left-hand side represents Δ*Pc*, the first term on the right-hand side is Δ*Pl* , and the second term corresponds to Δ*Pg*. In this equation, *σ* is the surface tension coefficient, *R*eff is the effective pore radius of the wick structure, *μl* is the liquid viscosity of working fluid, *L*eff is the effective length of heat pipe, *K* is the permeability, *Aw* is the cross-sectional area of the wick, *ρ<sup>l</sup>*

is the liquid density of working fluid, *m* . is the mass flow rate, *g* is the gravitational constant, and *φ* is the orientation angle with respect to the horizontal plane. The heat transport capacity of the heat pipe is directly proportional to the mass flow rate of the working fluid as follows:

$$
\mathcal{Q}\_{\text{max}} = h\_{\text{fg}} \dot{m} \tag{4}
$$

where *h*fg is the latent heat coefficient of working fluid. Combining Equations (3) and (4) yields the following equation for the capillary limit:

$$\mathcal{Q}\_{\text{max}} = \frac{KA\_{\text{w}}h\_{\text{tg}}\rho\_{\text{l}}}{\mu\_{\text{l}}L\_{\text{eff}}} \left[ \frac{2\sigma}{R\_{\text{eff}}} - \rho \text{g}L\_{\text{eff}}\sin\phi \right] \tag{5}$$

It should be underlined that the *K* and *R*eff are related to the microstructure of the wick; *h*fg, *σ*, *μl* , and *ρ<sup>l</sup>* are the fluid properties; and *L*eff and *Aw* represents the macroscopic geometry of the heat pipe. When the gravitational force can be neglected, the Equation (5) can be rewritten and each kind of parameters can be detached as independent term as follows:

$$\mathcal{Q}\_{\text{max}} = \left(\frac{2\sigma h\_{\text{lg}}\rho\_l}{\mu\_l}\right) \left(\frac{A\_{\text{w}}}{L\_{\text{eff}}}\right) \left(\frac{K}{R\_{\text{eff}}}\right) \tag{6}$$


**Figure 9.** *K* and *R*eff values for typical wick structures.

The first paragraphed term is a combination of the fluid properties, suggesting that the capillary limit of heat pipe is proportional to this term. This term is called the figure of merit of working fluid. The second paragraphed term is about the macroscopic geometry of the heat pipe. The last term is related to the wick microstructure, thus, in regard to the wick design, we have to maximize this term. This term is often called the capillary performance of wick. The permeability *K* is proportional to the pore characteristic length, whereas *R*eff is inversely proportional to the pore size. Therefore, the ratio between *K* and *R*eff captures a trade off between those two competing effects. The *K* and *R*eff values for representative wick structure are shown in **Figure 9**.

#### **3.3. Boiling limit**

Regarding the boiling limit, it has been postulated that the boiling limit occurs as soon as the bubble nucleation is initiated. Onset of nucleate boiling within the wick was considered as a mechanism of failure and was avoided. On the basis of that postulation, the following correlation for predicting boiling limit has been widely used [1]:

$$Q\_{\rm max} = \frac{2\pi L\_\ast k\_\ast T\_\ast}{h\_\text{ig} \rho\_\text{v} \ln\left(r\_i / r\_\text{v}\right)} \left(\frac{2\sigma}{r\_b} - P\_c\right) \tag{7}$$

where *Le* is the evaporator length, *ke* is the effective thermal conductivity of wick, *Tv* is the vapor core temperature, *h*fg is the latent heat, *ρv* is the vapor density, *rv* is the vapor core radius, *ri* is the radius of outer circle including the wick thickness, and *σ* is the surface tension coefficient. In Equation (7), important design parameters related to the wick microstructure are *rb* and *Pc*, which are bubble radius and capillary pressure, respectively. Even though Equation (7) is simple and in a closed form, it is difficult to implement this equation in which these parameters are quite arbitrary, and thus, it is difficult to exactly predict those values. To accurately determine *rb* and *Pc*, additional experiment should be performed [1]. Another fundamental problem also exists in which the nucleate boiling within the wick does not necessarily represent a heat transfer limit unless bubbles cannot escape from the wick, as indicated by several researchers [2]. Indeed, nucleate boiling may not stop or retard the capillary-driven flow in porous media according to the literatures. Some researchers even insisted that the nucleate boiling in the moderate temperature heat pipe wicks is not only tolerable but could also produce performance enhancement by significantly increasing the heat transfer coefficient over the conduction model and consequently reducing the wick temperature drop [3]. Therefore, new light should be shed on the model for the boiling limit. As illustrated in Equation (6), key parameters for capillary limit are *K* and *R*eff. Equation (7) shows that key parameter for boiling limit is *ke*, excluding the effect of permeability. Recently, it has been shown that the boiling limit does not occur with the nucleate boiling if the vapor bubble can escape the wick efficiently [4]. This suggests that the *K* is also an important parameter for the boiling limit.

## **4. Heat pipe designs**

#### **4.1. Heat pipe design procedure**

The design procedure of the heat pipe is as follows:


The followed subsections will be devoted to each procedure.

#### **4.2. Working fluid selection**

The first step for designing the heat pipe is to select the working fluid according to the operating temperature of the heat pipe. Each fluid has its vapor pressure profile with respect to the temperature. The vapor pressure increases as the temperature increases, and when the vapor pressure reaches the pressure of environment, boiling occurs. The heat pipe is designed to operate nearly at the boiling temperature for facilitating the heat transfer rate associated with the latent heat. Therefore, the working fluid should be selected under the consideration of the operating temperature of heat pipe. Various kinds of working fluids and their operating temperature ranges and corresponding inner pressures are shown in **Figure 10**. In case of water-based heat pipe that operates at the room temperature, the inner pressure of heat pipe is typically set to be approximately 0.03 bar for maximizing the thermal performance. When the operating temperature is 200°C, the inner pressure of the heat pipe should be set at roughly 16 bar. For cryogenic applications, helium or nitrogen gas is used. For medium or high temperature applications, liquid metals such as sodium and mercury are typically used. The inner pressure of heat pipe should be properly adjusted according to its operating temperature.


**Figure 10.** Operating temperature of working fluids.

**Figure 11.** Figure of merit numbers of working fluids.

The working fluid selection is also important in terms of the thermal performance. Equation (6) shows that the thermal performance of heat pipe is directly proportional to a fluid property, *ρl σh*fg/*μl* . This is often called the figure of merit of working fluid. **Figure 11** shows the figure of merit with respect to the temperature for various working fluids. As shown in this figure, occurring in low to moderate temperatures, water is the liquid with the highest figure of merit number. This is why the water is the most commonly used for heat pipe. Another common fluid is ammonia, which is used for low-temperature applications.


**Figure 12.** Material compatibility.

#### **4.3. Wick type selection**

The second step is to select the wick type. Typically, five selections can be considered: no wick (for thermosiphon), mesh screen wick, grooved wick, sintered particle wick, and heterogene‐ ous type wick. The reason we select the wick type prior to choosing the material is that the manufacturable microstructure is dependent on the material.

#### **4.4. Container and wick material selection**

After choosing the wick type, the material for container and wick is selected. Here, the major consideration is the compatibility between the working fluid and the material. Water–copper combination is known to have a good compatibility. On the other hand, the water is not compatible with aluminum due to unpreferred gas generation. The material compatibility with working fluid is shown in **Figure 12**. Copper is shown to be compatible with water, acetone, and methanol. The aluminum has good compatibility with acetone and ammonia, but not with water.

#### **4.5. Determination of diameter**

The next step is to determine the diameter of the heat pipe. The diameter becomes a major geometric parameter upon consideration of the vapor velocity. When the diameter of heat pipe is too small, the vapor velocity increases much, and compressibility effect appears, which in turn aggravates the performance of heat pipe significantly. Typically, it is known that the compressibility effect is negligible when the Mach number is less than 0.2. To fulfill this criterion, the following equation should be satisfied.

$$d\_{\vee} > \sqrt{\frac{20 \underline{Q\_{\text{max}}}}{\pi \rho\_{\text{v}} h\_{\text{tg}} \sqrt{\mathcal{V}\_{\text{v}} R\_{\text{v}} T\_{\text{v}}}} \tag{8}$$

where *dv* is the vapor core diameter, *Q*max is the maximum axial heat flux, *ρ<sup>v</sup>* is the vapor density, *γv* is the vapor-specific heat ratio, *h*fg is the latent heat of vaporization, *Rv* is the gas constant for vapor, and *Tv* is the vapor temperature.

#### **4.6. Determination of thickness**

As the heat pipe is like a pressure vessel, it must satisfy the ASME vessel codes. Typically, the maximum allowable stress at any given temperature can only be one-fourth of the material's maximum tensile strength. The maximum hoop stress in the heat pipe wall is given as follows [1]:

$$f\_{\text{max}} = \frac{P d\_o}{2t} \tag{9}$$

where *f*max is the maximum stress in the heat pipe wall; *P* is the pressure differential across the wall, which causes the stress; *do* is the heat pipe outer wall; and *t* is the wall thickness. The safety criterion is given as follows:

$$f\_{\text{max}} < \frac{\sigma\_Y}{4} \tag{10}$$

where *σY* is the yielding stress of the container material. Combining Equations (9) and (10) yields:

$$\frac{2Pd\_o}{\sigma\_Y} < t \tag{11}$$

#### **4.7. Wick design**

The maximum thermal performance of heat pipe is given in Equation (6). Let us retrieve Equation (6) as Equation (12).

$$\mathcal{Q}\_{\text{max}} = \left(\frac{2\sigma h\_{\text{tg}} \rho\_l}{\mu\_l}\right) \left(\frac{A\_{\text{w}}}{L\_{\text{eff}}}\right) \left(\frac{K}{R\_{\text{eff}}}\right) \tag{12}$$

In Equation (12), design parameters related to the wick are *K* and *R*eff. The *K* is known to proportional to the square of the characteristic pore size, whereas *R*eff is inversely proportional to the characteristic pore size. Therefore, the capillary performance, *K*/*R*eff, is directly propor‐ tional to the characteristic pore size. However, when the pore size is too large, the capillary pressure becomes too small so that the gravity effect cannot be overcome, which in turn makes the heat pipe useless. In addition, large pore size represents significant effect of inertia force. It should be noted that Equation (12) is derived under the postulation that the flow rate of working fluid is determined upon the balance between capillary force and viscous friction force where the inertia force is negligible in microscale flow. When the inertia force becomes significant, the thermal performance is significantly deviated from the prediction by Equation (12), in other words, is degraded much. For these reasons, the particle size of the sintered particle wick typically ranges from 40 μm to 300 μm. In case of looped heat pipe (LHP) where extremely high capillary pressure is required, nickel particles with 1–5 μm diameter are used.

#### **4.8. Heat sink–source interface design**

Besides design of heat pipe itself, the interfaces of heat pipe with heat sink–source are also of significant interest because the interfacial contact thermal resistance is much larger than that of heat pipe itself. The contact thermal resistance between the evaporator and the heat source and that between the condenser and the heat sink is relatively large. Therefore, they have to be carefully considered and minimized.

#### **4.9. Thermal resistance considerations**

**Figure 13.** Thermal resistance network.

Through Sections 4.1–4.7, only the maximum heat transport capability has been regarded as the performance index of the heat pipe. However, sometimes another performance index, the thermal resistance, is more important when the heat transfer rate is not of an important consideration while the temperature uniformization is more important. The thermal resistance of the heat pipe can be estimated based on the thermal resistance network, as shown in **Figure 13**. *Tx* is the heat source temperature, and *T*cf is the heat sink temperature. The subscripts *e* and *c* represent the evaporator and condenser, respectively. The subscripts *s*, *l*, and *i*represent the shell, liquid, and interface, respectively. The various thermal resistance components and correlations for predicting them are shown in **Figure 14**.


**Figure 14.** Thermal resistance correlations.

## **5. Application to electronics cooling**

The types of heat pipe applications to electronics cooling are as follows: use of flat-plate heat pipe, heat pipe–embedded heat spreader, block to fin, block to block, and fin to fin. The tubular heat pipe cannot solely used because its interface cannot be fully attached to the electronic devices having flat interface. For heat pipe to be adapted to the electronics cooling, the heat pipe itself should be formed into flat-plate type, or the tubular heat pipe should be fitted to rectangular-shaped based block, as shown in **Figure 15**. The heat pipe–embedded heat spreader is shown in **Figure 16**.

The block-to-fin applications are shown in **Figure 17**. The heat pipe has to be anyhow connected to the heat sink for the final heat dissipation to the air. The heat pipe–embedded block can be directly connected to the fin, as shown in this figure. In some applications such as sever computer and telecommunication unit handle a large amount of data, block-to-block module is employed, as shown in **Figure 18**. In some applications, the fin-to-fin module is also used.

**Figure 15.** Use of tubular heat pipe and flat-plate heat pipe.

**Figure 16.** Heat pipe–embedded heat spreaders.

**Figure 17.** Block-to-fin applications.

The use of heat pipe to electronics cooling is diversified into portable devices, VGA, mobile PC, LED projector and related devices, telecommunication repeater, and so on. The heat pipe is also widely employed in solar heat collection, snow melting, heat exchanger and related energy applications, and pure science applications demanding ultra-precise temperature control. Especially for the semiconductor devices whose performance and lifetime are sensitive to the temperature, heat pipe is an ultimate thermal solution. The use of heat pipe will surely expand, and it will gradually have more ripple effect in various industrial areas.

### **6. Summary**

In this chapter, the general aspects of heat pipes are introduced. The working principle of the heat pipe is based on two phase flows pumped by capillary pressure formed at the wick. The wick plays an important role in determining the thermal performance of the heat pipe. In this regard, various types of wick structures have been developed, such as mesh screen wick, grooved wick, and sintered particle wick. The thermal performance of heat pipe is generally determined by capillary limit, which can be readily predicted based on simple an‐ alytic method represented by Equation (6). Boiling limit is also important in high operation temperature. However, a definite model for the boiling limit is still not available. The heat pipe design starts with working fluid selection, followed by wick type and container materi‐ al selections, determining diameter and thickness, wick design, and heat sink–source inter‐ face design. The application of heat pipe to electronics cooling can be classified by the configuration: heat pipe–embedded spreader, block-to-block, block-to-fin, and fin-to-fin ap‐ plications.

## **Author details**

Chan Byon

Address all correspondence to: cbyon@ynu.ac.kr

School of Mechanical Engineering, Yeungnam University, Gyeongsan, South Korea

### **References**


## **Heat Pipes for Computer Cooling Applications**

Mohamed H.A. Elnaggar and Ezzaldeen Edwan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62279

#### **Abstract**

There is an increasing demand for efficient cooling techniques in computer industry to dissipate the associated heat from the newly designed and developed computer processors to accommodate for their enhanced processing power and faster operations. Such a demand necessitates researchers to explore efficient approaches for central processing unit (CPU) cooling. Consequently, heat pipes can be a viable and promising solution for this challenge. In this chapter, a CPU thermal design power (TDP), cooling methods of electronic equipments, heat pipe theory and operation, heat pipes components, such as the wall material, the wick structure, and the working fluid, are presented. Moreover, we review experimentally, analytically and numerically the types of heat pipes with their applications for electronic cooling in general and the computer cooling in particular. Summary tables that compare the content, methodology, and types of heat pipes are presented. Due to the numerous advantages of the heat pipe in electronic cooling, this chapter definitely leads to further research in computer cooling applications.

**Keywords:** Heat pipes, Electronic cooling, Wick structure, Working fluids, Computer cooling applications

#### **1. Introduction**

Effective cooling of electronic components is an important issue for successful functionality and high reliability of the electronic devices. The rapid developments in microprocessors necessitate an enhanced processing power to ensure faster operations. The electronic devi‐ ces have highly integrated circuits that produce a high heat flux, which leads to increase in the operating temperature of devices, and this results in the shortening of life time of the electronic devices [1]. Consequently, the need for cooling techniques to dissipate the associ‐ ated heat is quiet obvious. Thus, heat pipes have been identified and proved as one of the

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

viable and promising options to achieve this purpose prior to its simple structure, flexibility and high efficiency, in particularly. Heat pipes utilize the phase changes in the working fluid inside in order to facilitate the heat transport. Heat pipes are the best choice for cooling electronic devices, because depending on the length, the effective thermal conductivity of heat pipes can be up to several thousand times higher than that of a copper rod. The main perception of a heat pipe involves passive two-phase heat transfer device that can transfer large quantity of heat with minimum temperature drop. This method offers the possibility of high local heat removal rates with the ability to dissipate heat uniformly.

Heat pipes are used in a wide range of products such as air conditioners, refrigerators, heat exchangers, transistors, and capacitors. Heat pipes are also used in desktops and laptops to decrease the operating temperature for a better performance. Heat pipes are commercially presented since the mid-1960s. Electronic cooling has just embraced heat pipe as a dependa‐ ble and cost-effective solution for sophisticated cooling applications.

## **2. Thermal design power**

The thermal design power (TDP) has attracted the topmost interest of thermal solution designers, and it refers to the maximum power dissipated by a processor across a variety of applications [2]. The purpose of TDP is to introduce thermal solutions, which can inform manufacturers of how much heat their solution should dissipate. Typically, TDP is estimated as 20–30% lower than the CPU maximum power dissipation. Maximum power dissipation is the maximum power a CPU can dissipate under the worst conditions, such as the maximum temperature, maximum core voltage, and maximum signal loading conditions, whereas the minimum power dissipation refers to the power dissipated by the processor when it is switched into one of the low power modes. The maximum TDP ranges from 35 to 77 W for modern processors such as Intel® Core™ i5-3400 Desktop Processor Series [3], whereas the maximum TDP for modern notebook computers ranges from 17 to 35 W [4].

## **3. Cooling methods of electronic equipments**

The air cooling is the most important technology that contributes to the cooling of electronic devices [5]. In the past, there were three main ways to cool the electronic equipment: (1) passive air cooling that dissipates heat using the airflow generated by differences in temperature, (2) forced air cooling that dissipates heat by forcing air to flow using fans, and (3) forced liquid cooling that dissipates heat by forcing coolants like water to pass [6]. The conventional way to dissipate heat from desktop computers was forced convection, using a fan with a heat sink directly. The advantages, such as simple machining, simple structure, and lower cost, have made heat sinks with plate fins very useful in cooling of electronic devices [7]. However, with the smaller CPU size and increased power as encountered in modern computers, the heat flux at the CPU has been significantly increased [8]. At the same time, restrictions have been imposed on the size of heat sinks and fans and on the noise level associated with the increased fan speed. Consequently, there has been a growing concern for improved cooling techniques that suit the modern CPU requirements. As alternatives to the conventional heat sinks, twophase cooling devices, such as heat pipe and thermosyphon, have emerged as promising heat transfer devices with effective thermal conductivity over 200 times higher than that of copper [9].

## **4. Heat pipe theory and operation**

In order for heat pipe to operate, the maximum capillary pressure must be greater than the sum of all pressure drops inside the heat pipe to overcome them; thus, the prime criterion for the operation of a heat pipe is as follows

$$
\Delta P\_{\text{g}} \ge \Delta P\_{\text{l}} + \Delta P\_{\text{v}} + \Delta P\_{\text{g}} \tag{1}
$$

where, *ΔP*c is the maximum capillary force inside the wick structure; *ΔP*<sup>l</sup> is pressure drop required to return the liquid from the condenser to the evaporation section; *ΔP*<sup>v</sup> is the pressure drop to move the vapor flow from the evaporation to the condenser section; and *ΔP*g is the pressure drop caused due to the difference in gravitational potential energy (may be positive, negative, or zero, depends on the heat pipe orientation and a direction).

**Figure 1.** Heat pipe operation [10].

The basic steps of heat pipe operation are summarized as follows, with reference to **Figure 1** [10]:


The liquid pressure drop can be calculated from the empirical relation [11]:

$$
\Delta P\_l = \frac{\mu\_l L\_{\text{eff}} \mathcal{Q}}{\rho\_l K A\_{\text{w}} h\_{\text{fg}}} \tag{2}
$$

where μl =liquid viscosity, *L*eff=effective length of the heat pipe, ρ<sup>l</sup> =liquid density, *K*=wick permeability, *A*w=wick cross-sectional area, and *h*fg=heat of vaporization of liquid. The vapor pressure drop can be calculated from the following equation [12]:

$$
\Delta P\_{\rm v} = \frac{16\mu\_{\rm v} L\_{\rm cr} \mathcal{Q}}{2\left(\frac{D\_{\rm v}}{2}\right)^2 A\_{\rm v} \rho\_{\rm v} h\_{\rm g}} \tag{3}
$$

where μv=vapor viscosity, ρv=vapor density, *D*v=vapor space distance, and *A*v=vapor core cross-sectional area.

The maximum capillary pressure *ΔP*c generated inside the wick region is given by the Laplace– Young equation [13].

$$
\Delta P\_{\text{c}} = \frac{2\sigma\_{\text{l}}}{r\_{\text{eff}}} \tag{4}
$$

where σ<sup>l</sup> is surface tension and *r*eff is the effective radius of the pores of the wick.

The maximum achievable heat transfer by the heat pipe can be obtained from the equation [11]:

$$\mathcal{Q}\_{\text{max}} = \left(\frac{\rho\_l \sigma\_l h\_{\text{fg}}}{\mu\_l}\right) \left(\frac{A\_\text{w} K}{L\_{\text{eff}}}\right) \left(\frac{2}{r\_{\text{eff}}} - \frac{\rho\_l \text{g} L\_{\text{eff}} \sin \phi}{\sigma\_l}\right) \tag{5}$$

where φ is the angle between the axis of the heat pipe and horizontal (positive when the evaporator is above the condenser and it is negative if vice versa).

At horizontal orientation φ=0, equation (5) will become

$$\mathcal{Q}\_{\text{max}} = \left(\frac{\rho\_l \sigma\_l h\_{\text{fg}}}{\mu\_l}\right) \left(\frac{A\_{\text{w}} K}{L\_{\text{eff}}}\right) \left(\frac{2}{r\_{\text{eff}}}\right) \tag{6}$$

## **5. Advantages of heat pipe**

The heat pipe has many advantages compared with other cooling devices such as the follow‐ ing:


## **6. Heat pipes components**

To obtain sufficient information on a heat pipe, researchers should study its basic components, which play an important role in the efficiency of the pipe. Many researchers focused their research on the most important aspects of these components, such as the heat pipe container, the wick structure, and the working fluid. The studies of these components were through experimental and numerical analysis.

#### **6.1. The container or the wall of a heat pipe**

A container is a metal seal, which is capable of transferring heat through it to the working fluid. This metal has a good heat conductivity. Many factors affect the selection of the material of the container, e.g., wettability, strength to weight ratio, machinability and ductility, compati‐ bility with external environment and working fluid, thermal conductivity, weldability, and porosity. The container material must possess high strength to weight ratio, it must be nonporous to avoid any diffusion of vapor particles and, at the same time, should ensure minimum temperature difference between the wick and the heat source owing to its higher thermal conductivity.

#### **6.2. Wick or capillary structure**

The wick structure is the most important component of a heat pipe. It is responsible for the return of liquid from the condenser section to the evaporator section by the capillary property, even against the direction of gravity. Thus, the presence of wick makes the heat pipes operate in all orientations. The grooved wick, sintered wick, and screen mesh wick are the most important types of wick studied abundantly. These wick types are used widely in the elec‐ tronics industry and are detailed next.

#### *6.2.1. Metal sintered powder wick*

As shown in the **Figure 2**, this type of the wick has a small pore size, resulting in low wick permeability, leading to the generation of high capillary forces for antigravity applications. The heat pipe that carries this type of wick gives small differences in temperature between evaporator and condenser section. This reduces the thermal resistance and increases the effective thermal conductivity of the heat pipe.

Leong et al. [16] investigated the heat pipe with sintered copper wicks. Flat plate heat pipes with rectangular porous wicks were fabricated using copper powder (63 μm) sintered at 800 and 1000 °C. They used mercury intrusion porosimetry and scanning electron microscopy (SEM) techniques to investigate the porosity and pore size distribution in these wicks. Results indicated a unimodal pore size distribution with most pore sizes distributed within 30–40 μm. Moreover, the cylindrical wicks fabricated by injection molding technique with the same binder and sintering temperature were also compared. The calculated permeability values of the rectangular wicks were as good as those of the commercially produced cylindrical wicks. Compared with the wire mesh, the sintered wicks had smaller pores and had the controllability of porosity and pore size to get the best performance.

#### *6.2.2. Grooved wick*

The grooved wick is shown in **Figure 3**; this type of wick generates a small capillary driving force, but is appropriate or sufficient for low power heat pipes, which operates horizontally or with the direction of gravity.

**Figure 3.** Grooved wick [15].

Zhang and Faghri [17] simulated the condensation on a capillary grooved structure. They investigated the impacts of surface tension, contact angle, temperature drop, and fin thickness using the volume of fluid (VOF) model. Results indicated that the contact angels and heat transfer coefficients decreased when temperature difference increased. Significant increase in the liquid film thickness was also observed upon the increase of the fin thickness. Ahamed et al. [18] investigated thin flat heat pipe with the characteristic thickness of 1.0 mm, experimen‐ tally. A special fiber wick structure, which consisted of the combination of copper fiber and axial grooves as a capillary wick along the inner wall of the heat pipe, was used. The thin flat heat pipe was a straight one with rectangular cross section of 1.0 mm×5.84 mm. The heat pipe was made from copper pipe of 4 mm diameter, and the working fluid was pure deionized water. Their observation showed that the maximum heat that could be transported by the thin flat heat pipe of 1.0 mm thickness was 7 W. The thermal resistance of the heat pipe was 0.44 °C/W. The new fiber wick structure was also found to provide an optimum vapor space and capillary head for better heat transfer capabilities with less thermal resistance.

#### 58 Electronics Cooling

#### *6.2.3. Screen mesh wick*

**Figure 4** shows the screen mesh wick, which is used in many of the products, and they have demonstrated useful characteristics with respect to power transport and orientation sensitiv‐ ity.

**Figure 4.** Screen mesh wick [15].

Wong and Kao [19] presented visualization of the evaporation/boiling process and thermal measurements of horizontal transparent heat pipes. The heat pipes had two-layered copper mesh wick consisting of 100 and/or 200 mesh screens, glass tube, and water as the working fluid. Under lower heat load conditions, the thickness of the water film was less than 100 μm, and the nucleate boiling was observed at Q=40 W and Q=45 W, respectively. Optimal thermal characteristics were determined for the wick/charge combination, which provided the smallest thermal resistance across the evaporator with lowest overall temperature distribution. In contrast to lower load conditions, the higher heat loads with small charge led to partial dry out in the evaporator. However, under a larger charge, there was limited liquid recession with increasing heat load, and the bubble growth was found to be unsustainable and bursting violently. Liou et al. [20] presented the visualization and thermal resistance measurement for the sintered mesh–wick evaporator in flat plate heat pipes. The wick thickness was between 0.26 and 0.80 mm with different combinations of 100 and 200 mesh screens. Results showed that the increasing heat load tend to decrease the resistance of the evaporation until partial dry out occurred. Following this, the resistance of the evaporation started to increase slowly. Low permeability of the wick limited the reduction of evaporation resistance and prompted dry out.

The studies of wick types have the following main conclusions:

**•** Metal sintered powder wick has a small pore size, resulting in low wick permeability. This leads to generation of high capillary forces for antigravity applications. The heat pipe that carries this type of wick produces small temperature differences between evaporator and condenser section. Therefore, the thermal resistance is reduced, and the effective thermal conductivity of the heat pipe is increased.


#### **6.3. Working fluids**

Selection of the working fluid depends primarily on the operating vapor temperature range. This is because the basis in the operation of the heat pipe is the process of evaporation and condensation of the working fluid. The selection of appropriate working fluid must be done carefully, taking into account the following factors [21]:


The most important property of the working fluid is high surface tension so that the heat pipe works against gravity as it generates high force of the capillarity characteristic. **Table 1** summarizes the properties of some working fluids with their useful ranges of temperature [21].


**Table 1.** Heat pipe working fluid properties.

Distilled water is the most appropriate fluid for the heat pipes used for electronic equipment cooling. However, few researchers attempted to improve the thermal performance of the heat pipes by adding metal nanoparticles, which have good thermal conductors, such as silver, iron oxide, and titanium, to the distilled water in which the fluid is known as nanofluids. Some researchers looked into various ways to improve the performance of heat pipe through using different working fluids. Uddin and Feroz [22] experimentally investigated the effect of acetone and ethanol as working fluids on the miniature heat pipe performance. The experi‐ ments aimed to draw the heat from the CPU into one end of miniature heat pipes while providing the other end with extended copper fins to dissipate the heat into the air. The results illustrate that acetone had better cooling effect than ethanol. Fadhil and Saleh [23] reported an experimental study of the effect of ethanol and water as working fluids on the thermal performance of the heat pipe. The heat pipe was at the horizontal orientation during the experiments. The range of the heat flux changed within 2.8–13.13 kW/m2 , whereas all other conditions were constant. The results show that the thermal performance of the heat pipe with water as a working fluid was better than that with ethanol.

## **7. Types of heat pipes**

#### **7.1. Cylindrical heat pipe**

Cylindrical heat pipe with closed ends is a common and conventional type of heat pipe. It involves circulation of working fluid and a wick to return the liquid. Basically, it consists of three sections, namely evaporator, adiabatic, and condenser, as shown in **Figure 5**.

El-Genk and Lianmin [25] reported on the experimental investigation of the transient response of cylindrical copper heat pipe with water as working fluid. The copper heat pipe with copper screen wick consisted of two layers of 150 meshes. Results showed that the temperature of the vapor was uniform along the heat pipe whereas the wall temperature drop was very small (maximum variation less than 5 K) between the evaporator section and the condenser section. The steady-state value of the vapor temperature was increased when the heat input was increased or the cooling water flow rate was decreased. Said and Akash [26] experimentally studied the performance of cylindrical heat pipe using two types of heat pipes with and without wick, and water as the working fluid. They also studied the impact of different inclined angles, such as 30°, 60°, and 90°, with the horizontal on the performance of heat pipe. Results showed that the performance of heat pipe with wick was better than the heat pipe without wick. The overall heat transfer coefficient was the best at the angle of 90°.

#### **7.2. Flat heat pipes**

Wang and Vafai [27] presented an experimental investigation on the thermal performance of asymmetric flat plate heat pipe. As shown in **Figure 6**, the flat heat pipe consists of four sections with one evaporation section in the middle and three condenser sections. The heat transfer coefficient and the temperature distribution were obtained. The results indicated that the temperature was uniform along the wall surfaces of the heat pipe, and the porous wick of the evaporator section had significant effect on the thermal resistance. The heat transfer coefficient was also found to be 12.4 W/m2 °C at the range of input heat flux 425–1780 W/m2 .

**Figure 6.** Schematic of the flat plate heat pipe: (a) geometry of the heat pipe and (b) cross-sectional view of the heat pipe [27].

Thermal performance of a flat heat pipe thermal spreader was investigated by Carbajal et al. [28]. They carried out quasi-three-dimensional numerical analysis in order to determine the field variable distributions and the effects of parametric variations in the flat heat pipe system. Investigations showed that flat heat pipe operating as a thermal spreader resulted in more uniform temperature distribution at the condenser side when compared to a solid aluminum plate having similar boundary conditions and heat input.

#### **7.3. Micro-heat pipes**

Micro-heat pipes differ from conventional heat pipes in the way that they replace wick structure with the sharp-angled corners, which play an important role in providing capillary pressure for driving the liquid phase. Hung and Seng [29] studied the effects of geometric design on thermal performance of star-groove micro-heat pipes. As shown in **Figure 7**, three different types of cross-sectional shapes of micro-heat pipes such as square star (4 corners), hexagonal star (6 corners), and octagonal star (8 corners) grooves with corner width w, were considered. Accordingly, the corner apex angle 2θ was varied from 20° to 60°. At steady-state mode, one-dimensional mathematical model was developed to yield the heat and fluid flow characteristics of the micro-heat pipe. Results indicated that the geometrical design of the stargroove micro-heat pipes provides a better insight on the effects of various geometrical parameters, such as cross-sectional area, total length, cross-sectional shape, number of corners, and acuteness of the corner apex angle.

**Figure 7.** (a) Geometry of different cross-sectional shapes of micro-heat pipe: (i) square star groove, (ii) hexagonal star groove, (iii) octagonal star groove, and (iv) equilateral triangle. (b) Schematic diagram of optimally charged equilateral triangular and star-groove micro-heat pipes [29].

#### **7.4. Oscillating (pulsating) heat pipe**

Oscillating (pulsating) heat pipe (OHP) is one of the promising cooling devices in modern application that can transport heat in quick response in any orientation, where the oscillating phenomena offer an enhanced heat transfer mechanism as shown in **Figure 8**. The unique feature of OHPs, compared with conventional heat pipes, is that there is no wick structure to return the condensate to the heating section; thus, there is no countercurrent flow between the liquid and vapor [30]. The fluctuation of pressure waves drives the self-exciting oscillation inside the heat pipe, and the oscillator accelerates end-to-end heat transfer [31]. The pressure change in volume expansion and contraction during phase change initiates and sustains the thermally excited oscillating motion of liquid plugs and vapor bubbles between evaporator and condenser [32], this is because both phases of liquid and vapor flow has the same direction. The thermally driven oscillating flow inside the capillary tube effectively produces some free surfaces that significantly enhance the evaporating and the condensing heat transfer.

**Figure 8.** Schematic of an oscillating heat pipe [33].

Although many of researchers have considered the effect of OHP parameters on thermal performance, such as internal diameter, number of turns, filling ratio, and nanofluids, the development of comprehensive design tools for the prediction of OHP performance is still lacking [30]. Moreover, according to Zhang and Faghri [34], the previous theoretical models of OHPs were mainly lumped, one-dimensional, or quasi-one-dimensional, and many unrealistic assumptions were predominantly presented.

## **8. Mathematical modelling and numerical simulations**

Mathematical models of heat pipes are categorized into analytical method and numerical simulations. The analytical method validates the experimental and simulation results, which cannot be measured experimentally, such as pressure and velocity of working fluid inside the heat pipe. Numerical simulation is vital for investigating the thermal behavior of the working fluid inside the heat pipes and predicting the temperature of heat pipe wall, from which the thermal resistance and the amount of heat transmitted by the heat pipes can be calculated. Moreover, characterization of the liquid inside the wick, and predictions of the pressures and velocities of vapor and liquid, enables designing a highly efficient heat pipe for cooling electronic devices.

#### **8.1. Assumptions of the mathematical model**

The following assumptions were made for the mathematical formulation:


#### **8.2. Governing equations**

Based on the above assumptions, the continuity, the momentum, and energy equations are listed as follows:

#### *8.2.1. Vapor region*

*Continuity*:

$$\frac{\mu\_v}{\infty} + \frac{\nu\_v}{\nu} = 0\tag{7}$$

where, *u* and *ν* are components of velocity in *x* and *y* directions, respectively.

Momentum:

#### Heat Pipes for Computer Cooling Applications http://dx.doi.org/10.5772/62279 65

$$
\rho\_v \rho\_v \left( \mu\_v \frac{\mu\_v}{\mathbf{x}} + \nu\_v \frac{\mu\_v}{\mathbf{y}} \right) = \frac{-p}{\mathbf{x}} + \mu\_v \left( \frac{\mu\_v^2}{\mathbf{x}^2} + \frac{\mu\_v^2}{\mathbf{y}^2} \right) \tag{8}
$$

$$
\rho \,\rho \left( \mu\_\text{v} \frac{\nu\_\text{v}}{\text{x}} + \nu\_\text{v} \frac{\nu\_\text{v}}{\text{y}} \right) = \frac{-p}{\mathcal{Y}} + \rho \,\text{g} + \mu\_\text{v} \left( \frac{\nu\_\text{v}^2}{\text{x}^2} + \frac{\nu\_\text{v}^2}{\text{y}^2} \right) \tag{9}
$$

*Energy*:

$$\rho\_v c\_p \left(\mu\_v \frac{T}{\mathbf{x}} + \nu\_v \frac{T}{\mathbf{y}}\right) = k\_v \left(\frac{T^2}{\mathbf{x}^2} + \frac{T^2}{\mathbf{y}^2}\right) \tag{10}$$

where, *g* is the acceleration of gravity, *ρ<sup>v</sup>* vapor density, μv is the effective viscosity of vapor for laminar case is merely the dynamic viscosity, *c*<sup>p</sup> specific heat, and *k*<sup>v</sup> is thermal conduc‐ tivity of vapor.

#### *8.2.2. Liquid wick region*

*Continuity*:

$$\frac{\mu\_1}{\mu} + \frac{\nu\_1}{\nu} = 0\tag{11}$$

where, *u* and *ν* are components of velocity in *x* and *y* directions, respectively.

*Momentum*:

$$\rho\_l \left( u\_l \frac{u\_l}{\varkappa} + v\_l \frac{u\_l}{\varkappa} \right) = \frac{-P\_l}{\varkappa} + \mu\_l \left( \frac{u\_l^2}{\varkappa^2} + \frac{u\_l^2}{\varkappa^2} \right) + R\_x \tag{12}$$

$$
\rho\_l \left( \mathbf{u}\_l \frac{\mathbf{v}\_l}{\mathbf{x}} + \mathbf{v}\_l \frac{\mathbf{v}\_l}{\mathbf{y}} \right) = \frac{-P\_l}{\mathbf{y}} + \rho\_l \mathbf{g} + \mu\_l \left( \frac{\mathbf{v}\_l^2}{\mathbf{x}^2} + \frac{\mathbf{v}\_l^2}{\mathbf{y}^2} \right) + R\_y \tag{13}
$$

*Rx* and *Ry* are distributed resistance components in *x* and *y* directions, respectively. A dis‐ tributed resistance is a proper method to estimate the effect of porous media.

Energy:

$$\rho\_l \rho c\_{p,l} \left( u\_l \frac{T\_l}{\mathbf{x}} + \mathbf{v}\_l \frac{T\_l}{\mathbf{y}} \right) = k\_e \left( \frac{T\_1^2}{\mathbf{x}^2} + \frac{T\_1^2}{\mathbf{y}^2} \right) + \mathbf{Q}\_\mathbf{v} \tag{14}$$

where, *g*, *ρ*, *μ*, *C*p, *k*e, and *Q*<sup>v</sup> are gravitational acceleration, density, dynamic viscosity, specific heat, effective thermal conductivity for liquid wick structure, and volumetric heat flux, respectively. Subscripts v and l refers to vapor and liquid regions, respectively. *k*e is the effective thermal conductivity of the liquid wick structure for sintered powder wick, as expressed by [12]:

$$k\_{\rm c} = \frac{k\_{\rm l} \left\lfloor \left(2k\_{\rm l} + k\_{\rm w}\right) - 2\left(1 - \phi\right)\left(k\_{\rm l} - k\_{\rm w}\right) \right\rfloor}{\left(2k\_{\rm l} + k\_{\rm w}\right) + \left(1 - \phi\right)\left(k\_{\rm l} - k\_{\rm w}\right)} \tag{15}$$

For screen mesh wick, *k*e is calculated from [12]:

$$k\_{\varepsilon} = \frac{k\_l \left[ \left( k\_l + k\_w \right) - \left( 1 - \phi \right) \left( k\_l - k\_w \right) \right]}{\left( k\_l + k\_w \right) + \left( 1 - \phi \right) \left( k\_l - k\_w \right)} \tag{16}$$

where, *φ* is porosity and *k*<sup>l</sup> and *k*w are thermal conductivity of liquid and wick material, respectively.

The steady-state thermal conductivity equation to predict the wall temperature is as follows:

$$k\_s \left(\frac{T\_s^2}{\varkappa^2} + \frac{T\_s^2}{\varkappa^2}\right) = 0\tag{17}$$

where, *k*s is solid thermal conductivity and *T*s is wall (surface) temperature.

#### **8.3. Boundary conditions**

At both ends of the heat pipe, *u*v=*ν*v=*u*<sup>l</sup> =*ν*<sup>l</sup> =0, and Pv=Pl .

At the centerline of evaporator section, *ν*v= 0, *<sup>u</sup>*<sup>v</sup> *<sup>y</sup>* =0, and *<sup>T</sup> <sup>y</sup>* =0.

At the centerline of condenser section, *u*v=0, *<sup>v</sup>*<sup>v</sup> *<sup>y</sup>* =0, and *<sup>T</sup> <sup>x</sup>* =0.

$$\text{At } r = \mathbb{R}\_{\text{w}} \text{ } \mu\_1 = \nu\_1 = 0.$$

At the adiabatic section, *ρ*v*ν*v=*ρ*<sup>l</sup> *ν*l =0.

The continuity of mass fluxes in *y* direction at the vapor–liquid interface yields

$$
\rho\_\mathbf{v} \nu\_\mathbf{v} = \rho\_\mathbf{l} \nu\_\mathbf{l} = -\rho\_\mathbf{v} \nu\_\mathbf{1}
$$

where, *ν*1 is the vapor injection velocity expressed as [35]:

$$\nu\_1 = \frac{\mathcal{Q}\_{\rm tp}}{2\,\rho\_\mathrm{v}\pi R\_\mathrm{v}L\_\mathrm{c}h\_\mathrm{fg}} \tag{18}$$

Similarly, the continuity of mass fluxes in *x* direction at the vapor–liquid interface yields *ρ*v*u*v=*ρ*<sup>l</sup> *u*l =*ρ*v*u*<sup>1</sup>

where, *u*1 is the vapor suction velocity as given in the study by Kaya and Goldak [35]:

$$\mu\_1 = \frac{\mathcal{Q}\_{\rm tp}}{2\,\rho\_\mathrm{v}\pi R\_\mathrm{v}L\_\mathrm{c}h\_\mathrm{fg}} \tag{19}$$

The interface temperature (∫*T*) is calculated by the Clausius–Clapeyron equation, assuming the saturation temperature (*T*0) and vapor pressure (*P*0) at the liquid–vapor interface [36]:

$$\int = \frac{1}{\frac{1}{T\_0} - \frac{R}{h\_{\otimes}} \ln \left(\frac{P\_\upsilon}{P\_0}\right)}\tag{20}$$
 
$$T$$

For the solid–liquid interface:

At the evaporator part, *K*<sup>e</sup> *T*l *<sup>y</sup>* =*k*<sup>s</sup> *T*s *y* At the condenser part, *K*<sup>e</sup> *T*l *<sup>x</sup>* =*k*<sup>s</sup> *T*s *x*

where *K*e is the effective thermal conductivity of the liquid wick region, and *K*eff is the effective thermal conductivity of the whole heat pipe.

At the external heat pipe wall={ Evaporator *<sup>k</sup>*<sup>s</sup> *T <sup>y</sup>* =*q*<sup>e</sup> Adiabatic *<sup>T</sup> <sup>y</sup>* <sup>=</sup> <sup>0</sup> <sup>∧</sup> *<sup>T</sup> <sup>x</sup>* =0 Condenser−*k*<sup>s</sup> *T <sup>x</sup>* =*h* (*T*s−*T*a) }

where, *h* is convection heat transfer coefficient, and *T*w and *T*a are wall surface and ambient temperatures, respectively.

Mistry et al. [37] carried out two-dimensional transient and steady-state numerical analysis to study the characteristics of a cylindrical copper-water wicked (80 mesh SS-304 screen) heat pipe with water as a coolant at a constant heat input. Finite difference and Euler's explicit method (marching scheme) was used to solve the governing equations. As shown in **Figure 9**, a two-dimensional computational study using the concept of a growing thermal layer in the wall and the wick region was carried out. The transient axial temperature distributions were measured, and all the three sections of the heat pipe were compared with the numerical solution of the developed two-dimensional model. The time required to reach steady state was obtained. The transient and steady-state predictions of temperatures from the twodimensional model were in close agreement with the experimentally obtained temperature profiles.

**Figure 9.** Coordinate system of the heat pipe [38].



\*H, horizontal orientation; I, inclined orientation; \*\*SS, steady state; and T, transient.

**Table 2.** An overview of some mathematical studies on heat pipes.

As shown in **Table 2**, the three-dimensional model received a little attention compared to the two-dimensional model. Additionally, most of the studies addressed horizontal heat pipes that cover both transient and steady-state cases.

## **9. Heat pipe for computer cooling applications (desktop and notebook)**

Due to the high effective thermal conductivity of heat pipes compared to that of traditional heat sinks, heat pipes have been proposed and selected for electronic cooling. Therefore, the heat pipe transfers and dissipates the heat very fast. Many researchers focused their studies on using the heat pipe for cooling of electronic devices, and all of them proved that the heat pipe is the best tool for cooling the electronic devices such as desktop and notebook computers. Cooling fins equipped with heat pipes for high power and high temperature electronic circuits and devices were simulated by Legierski and Wiecek [43], and the superiority of the proposed system over the traditional devices was demonstrated. Kim et al. [44] developed a cooling module in the form of remote heat exchanger using heat pipe for Pentium-IV CPU as a means to ensure enhanced cooling and reduced noise level compared to the fan-assisted ordinary heat sinks. Saengchandr and Afzulpurkar [45] proposed a system that combines the advan‐ tages of heat pipes and thermoelectric modules for desktop PCs. As shown in **Figure 10**, the usage of the heat pipes with heat sink could enhance the thermal performance [46].

**Figure 10.** Heat pipe heat sink solution for cooling desktop PCs [47].

Yu and Harvey [47] designed a precision-engineered heat pipe for cooling Pentium II in Compact PCI. In this work, the design criteria, such as the maximum temperature, thermal transfer plate with a heat load, the maximum ambient air temperature, and the total thermal resistance of the solution, were considered for the processor module. It was observed that both thermal and mechanical management of the system was improved using the heat pipe. Kim et al. [44] presented the heat pipe cooling technology for CPU of desktop PC. They had developed a cooler using heat pipe with heat sink to decrease the noise of the fan. Results showed that the usage of heat pipe for desktop PC CPU cooling would increase the dissipated heat without the need for high speed fan. Thus, the problem of the noise generated by the traditional heat sink cooling was solved. Additionally, Closed-end Oscillating Heat pipe (CEOHP) used for CPU cooling of desktop PC was presented by Rittidech and Boonyaem [48]. As shown in **Figure 11**, the CEOHP kit is divided into two parts, i.e., the evaporator is 0.05 m long and a condenser section is 0.16 m long with and a vertical orientation. They selected R134a as the working fluid with filling ratio of 50%. The CEOHP kit should transfer at least 70 W of heat power to work properly. The CPU chip with a power of 58 W was 70°C. The results indicate that the cooling performance increases when the fan speed increases, where the fan speed of 2000 and 4000 rpm were employed. The thermal performance using CEOHP cooling module was better than using conventional heat sink.

**Figure 11.** Prototype: (a) aluminum base plate, (b) copper fin, (c) CEOHP. [49].

Recently, heat sinks with finned U-shape heat pipes have been introduced for cooling the highfrequency microprocessors such as Intel Core 2 Duo, Intel Core 2 Quad, AMD Phenom series, and AMD Athlon 64 series, as reported by Wang et al. [49], Wang [50], and Liang and Hung [51]. Wang et al. [49] experimented on the horizontal twin heat pipe with heat sink. The heat input was transferred from CPU to the base plate and from the base plate to the heat pipes and heat sinks simultaneously. The heat was dissipated from fins to the surrounding by forced convection. As shown in **Figure 12**, experiments were conducted in two stages, in which the first stage measured the temperature for heat pipes only to calculate its thermal resistance. The second stage aimed to measure the temperature for heat sink without and with heat pipes in order to calculate their thermal resistances. It was observed that 64% of the total dissipated heat was transported from CPU to the base plate and then to fins, whereas 36% was transferred from heat pipes to fins. The lowest value of the total thermal resistance for the heat pipes with heat sink was 0.27°C/W.

**Figure 12.** Heat sink without and with embedded heat pipes [50].

The investigations by Elnaggar et al. [52] on the experimental and finite element (FE) simula‐ tions of vertically oriented finned U-shape multi-heat pipes for desktop computer cooling are shown in **Figure 13a**. The total thermal resistance was found to decrease with the increase in heat input and coolant velocity. Moreover, the vertical mounting demonstrated enhanced thermal performance compared with the horizontal arrangement. The lowest total thermal resistance achieved was 0.181°C/W with heat load of 24 W and coolant velocity of 3 m/s. This study was further pursued by Elnaggar et al. [53] to determine the optimum heat input and the cooling air velocity for vertical twin U-shape heat pipe with the objective of maximizing the effective thermal conductivity as shown in **Figure 13b**.

**Figure 13.** Finned U-shape heat pipe for desktop computer cooling [53, 54]. (a) Finned U-shape multi-heat pipe [53]. (b) Finned U-shape twin heat pipe [54].


A summary of studies on heat pipe with heat sink for CPU PC cooling are listed in **Table 3**.

**Table 3.** A summary of studies on heat pipe with heat sink for CPU PC cooling.

The following conclusions can be derived from the summary of heat pipe with heat sink used in CPU PC cooling:


**Figure 14.** Laptop's cooling using a heat pipe with heat sink [56].

The processor's surface in notebook or laptop computers, where most heat is generated, is usually small approximately 10 mm×10 mm. For useful cooling, the heat must spread over a larger surface area away from the processor, as the space available near the processor is limited as shown in **Figure 14**. Therefore, heat must be drawn from the processor and conveyed to a place from where it can be dissipated by conventional means. This task is successfully achieved by a heat pipe as it can be accommodated in a highly constrained space in such a way that its evaporator section communicates with the heat source while the finned condenser section is exposed to the sink [55].

## **10. Conclusion**

In this chapter, we presented a TDP for cooling the CPU, cooling methods of electronic equipments, heat pipe theory and operation, heat pipes components, such as the wall material, the wick structure, and the working fluid. Moreover, we reviewed experimentally, analytically and numerically the types of heat pipes with their applications for electronic cooling in general and the computer cooling in particular. Clearly, the heat pipe can be regarded as a promising way for cooling electronic equipments. Due to its simplicity, it can work in any orientation and can transfer heat from a place where there is no opportunity and possibility to accommodate a conventional fan, such as notebooks or laptops. Finally, we believe this work would definitely open ways for further research in accordance with the growing attention for the use of heat pipes in electronic cooling.

## **Author details**

Mohamed H.A. Elnaggar\* and Ezzaldeen Edwan

\*Address all correspondence to: mohdhn@yahoo.com

Palestine Technical College, Deir EL-Balah, Gaza Strip, Palestine

## **References**


Systems, 2000. ITHERM 2000. The Seventh Intersociety Conference on. 2000; 2: 102–105 vol. 102.


## **Chapter 5**

## **MEMS-Based Micro-heat Pipes**

Qu Jian and Wang Qian

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62786

#### **Abstract**

Micro-electro-mechanical systems (MEMS)-based micro-heat pipes, as a novel heat pipe technology, is considered as one of the most promising options for thermal control applications in microelectronic circuits packaging, concentrated solar cells, infrared detectors, micro-fuel cells, etc. The operating principles, heat transfer characteristics, and fabrication process of MEMS-based micro-grooved heat pipes are firstly intro‐ duced and the state-of-the-art of research both experimental and theoretical is thoroughly reviewed. Then, other emerging MEMS-based micro-heat pipes, such as micro-capillary pumped loop, micro-loop heat pipe, micro-oscillating heat pipe, and micro-vapor chamber are briefly reviewed as well. Finally, some promising and innovatory applications of the MEMS-based micro-heat pipes are reported. This chapter is expected to provide basic reference for future researches.

**Keywords:** micro-heat pipe, thermal control, capillary limitation, micro-cooler, MEMS

### **1. Introduction**

Nowadays, the thermal management of electronics/optoelectronics remains to be a great challenge due to the continuous increasing heat flux to be dissipated with diminishing space associated with rapid advances in the microelectronic fabrication and packaging technology. Generally, the thermal control at the system level is not a serious problem since adequate conventional cooling schemes are available [1]. Cooling at the chip level that maintains both chip maximum temperature and temperature gradient at acceptable levels are in great demands. Many efforts have been made in the past two decades to develop novel micro-cooling technol‐ ogies capable of removing larger amount of heat from chips [2–5], among which micro-heat pipes (MHPs) are considered as one of the most promising solutions.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

MHPs, envisioned very small heat transfer components incorporated as an integral part of semiconductor devices as illustrated in **Figure 1**, have attracted considerable attention since they were first introduced by Cotter [6]. A MHP is also referred to micro-grooved heat pipe as depicted by Suman [7] and essentially has convex but cusped cross sections with dimension characteristics subject to the criterion given by Babin et al. [8]

$$\frac{r\_c}{r\_h} \ge 1\tag{1}$$

where *r* c and *r* h are the capillary and hydraulic radius, respectively. Accordingly, the hydraulic radius of the total flow passage in a MHP is comparable in magnitude to the capillary radius of the vapor–liquid interface. This dimensionless expression better defines a MHP and helps to differentiate between small versions of conventional heat pipes and a veritable MHP. Typically, the cross-sectional dimensions of MHPs are in the range of 10–500 μm and lengths of up to several centimeters [9]. A MHP is so small that it does not necessitate additional wicking structures on the inner wall as used by conventional heat pipes to assist the return of condensate to the evaporator. Instead, the capillary forces are largely generated in the sharp edges of diverse small noncircular channel cross sections as illustrated in **Figure 2**, which serve as liquid arteries. The maximum heat flux dissipated using these micro-devices are reported to be as high as 60 W/cm2 [11].

**Figure 1.** Micro-heat pipe array in silicon wafer.

Actually, MHPs are suitable for the direct heat removal from semiconductor devices because they could be fabricated and integrated into them, as envisioned by Cotter [6], on the basis of micro-electro-mechanical systems (MEMS) technology and work as thermal spreaders [12]. The advantages of MEMS-based MHPs mainly includes as follows: (1) It allows for precise temperature control at the chip level; (2) the overall cooling is more efficient because specific heat sources within the electronics package may be targeted and reduce the contact thermal resistance; (3) the overall size of the electronic system can be kept small and achieve material compatibility; and (4) easy to large scale replication and mass production. Due to the compact size, high local heat removal rates and can be used to effectively lower chip maximum temperature and attain temperature uniformity, MEMS-based MHPs could be considered as a promising option to meet future chip-level cooling demands.

**Figure 2.** Cross-sections of individual micro-grooved heat pipes: (a, b) triangular section; (c, d) rectangular section; (e, f) square section; (g) trapezoidal section; (h) circular section [10].

For all practical situations, MHP is a general name for heat pipes with micro-wicks and mini-/micro-tubes in many references, and a heat pipe that satisfies the Bond number (*Bo* =(*ρ*l−*ρ*g)*gr*<sup>h</sup> <sup>2</sup> / *σ*) to be on the order of 1 or less or capillary action dominates gravity can be termed as MHPs [7, 13]. The published reviews of MHPs were largely related to microgrooved heat pipes [14–16], and there is no comprehensive introduction on MEMS-based MHPs. Moreover, the concept of MEMS-based MHPs, in this chapter, are not simply limited to micro-grooved heat pipes etched on silicon wafers but also other novel types that fabricated through MEMS technology. The overall size of a MEMS-based heat pipe device should be comparable to that of an electronic chip, regardless of having wicking struc‐ tures or not.

In this chapter, we present a review on the MEMS-based MHPs that begin with a brief introduction of micro-grooved heat pipes, including working principles, heat transport limitations, and fabrication approach. The following section focuses on the state-of-the-art of research on MEMS-based micro-grooved heat pipes both experimentally and numerically, and then advances made in some other emerging MEMS-based MHPs. Meanwhile, some promis‐ ing and potential applications of MEMS-based MHPs are also reported. It is expected to provide a basis for MEMS-based MHP design, performance improvement, and further expansion in its applications.

## **2. Micro-grooved heat pipe**

#### **2.1. Fundamental operating principles**

The fundamental operating principles of micro-grooved heat pipes are essentially the same as those occurring in conventional heat pipes and can be easily understood by using a triangular cross section MHP as illustrated in **Figure 3**. Heat applied to one end of the MHP, called evaporator, vaporizes the liquid in that region and pushes the vapor toward the cold end, called condenser, where it condenses and gives up the latent heat of vaporization. In between the evaporator and the condenser is a heat transport section, called the adiabatic section, which may be omitted in some cases. MHPs do not contain any wicking structures, but consist of small non-circular channels and the role of wicks in conventional heat pipes gives way to the sharp-angled corner regions, serving as liquid arteries. The vaporization and condensation processes cause the curvature of liquid–vapor interface (see **Figure 3**) in the corner regions to change continually along the passage and result in a capillary pressure difference between the hot and cold ends. The capillary force generated from the corner regions pump the liquid back to the evaporator and the circulation of working fluid inside the MHP accompanied by phase change is then established [17, 18].

**Figure 3.** Schematic diagram of a micro-heat pipe with triangular cross-section.

#### **2.2. Heat transport limitations**

The operation and performance of heat pipes are dependent on many factors such as the tube size, shape, working fluid, and wicking structure. The maximum heat transport capability of a heat pipe operating at steady state is governed by a number of limiting factors, including the capillary, sonic, entrainment, and boiling limitations [18]. Theoretical and fundamental phenomena that cause each of these heat pipe limitations have been the subject of a number of investigations for conventional heat pipes. The representative work was given and dis‐ cussed by many authors [19], while only a limited number concern the operating limitations in a MHP [20]. The experimental investigation by Kim and Peterson [21] revealed that the capillary limitation occurred before entrainment and boiling limitations. When the heat input is larger than a maximum allowable heat load, capillary limitation occurs and becomes the most commonly encountered limitation to the performance of a MHP [22, 23], which causes the dry-out of the evaporator and degrades the thermal performance significantly. As a result, the capillary limitation is the primary concern of MHP design and operation according to its working principles. It can be concluded from the operating principles that the primary mechanism by which MHPs operates result from the difference in the capillary pressure across the liquid–vapor interfaces in the evaporator and condenser sections. For proper operation, the capillary pressure difference should be greater than the sum of all the pressure losses throughout the liquid and vapor flow passages. The gravity force is usually not taken into account in two-phase micro-devices compared to surface tension, and thus, the hydrostatic pressure drop can be neglected [24]. Hence, the relationship can be expressed mathematically as follows

$$
\Delta p\_{\rm c} \ge \Delta p\_{\rm l} + \Delta p\_{\rm v} \tag{2}
$$

where *Δp* <sup>c</sup> is the net capillary difference, *Δp* <sup>l</sup> and *Δp* <sup>v</sup> are the viscous pressure drops in the liquid phase and vapor phase, respectively.

The left-hand side in Eq. (2) at a liquid–vapor interface can be estimated from Laplace-Young equation, and for most MHP applications it can be reduced to:

$$
\Delta p\_{\rm c} = \sigma \left( \frac{1}{r\_{\rm ce}} - \frac{1}{r\_{\rm ce}} \right) \tag{3}
$$

where *r*ce and *r*cc represent the minimum meniscus radius appearing in the evaporator and maximum meniscus radius in the condenser, respectively. Both values depend on the shape of the corner region and the amount of liquid charged to the heat pipe.

For steady-state operation with constant heat addition and removal, the viscous pressure drop occurring in liquid phase is determined by

$$
\Delta p\_{\rm l} = \left(\frac{\mu\_{\rm l}}{KA\_{\rm l}h\_{\rm fg}\rho\_{\rm l}}\right) L\_{\rm eff} q \tag{4}
$$

where *L* eff is the effective heat pipe length defined as:

$$L\_{\rm eff} = 0.5(L\_{\rm e} + L\_{\rm c}) + L\_{\rm a} \tag{5}$$

The viscous vapor pressure drop can be calculated similarly to the liquid vapor drop but is more complicated due to the mass addition and removal in the evaporator and condenser, respectively, as well as the compressibility of the vapor phase. Consequently, the dynamic pressure should be included for a more accurate computation and thus elaborately analyzed by several researchers [17]. The resulting expression, for practical values of Reynolds number and Mach number, is similar to the liquid pressure drop and can be expressed as follows:

$$
\Delta p\_{\rm v} = \left(\frac{C(f \text{ Re})\_{\rm v} \mu\_{\rm v}}{2r\_{\rm h,v}^2 A\_{\rm g} h\_{\rm g} \rho\_{\rm v}}\right) L\_{\rm eff} q \tag{6}
$$

where *r*h,v is the hydraulic radius of the vapor space and *C* is a constant that depends on the Mach number [12, 25].

#### **2.3. Fabrication process of MEMS-based micro-grooved heat pipes**

In 1991, Peterson et al. [26] initialized the concept of using micro-grooved heat pipes as an integral part of the semiconductor devices. Normally, MEMS-based MHPs with hydraulic diameters on the order of 50–300 μm are directly etched into silicon wafers, and the direction‐ ally dependent wet etching or deep reactive ion etching (DRIE) processes are commercially available and widely utilized to create a series of parallel micro-grooves which shape the microdevices [27–30]. The wet chemical etching process could create trapezoidal or triangular grooves, allowing etching of silicon wafers in one particular direction at a higher rate as compared to other directions, while DRIE process that uses physical plasma tool generates rectangular grooves. Once the micro-grooves are etched into the silicon wafer, a Pyrex 7740 glass cover plate is often bonded to the surface to form the closed channels based on anodic bonding technique for the visualization of two-phase flow in MHPs.

The lithographic masking techniques, coupled with an orientation-dependent etching techni‐ que, are typically utilized and Peterson [17] has summarized this processes. **Figure 4** gives an example of six major fabrication process with respect to a MEMS-based MHP having trape‐ zoidal cross sections, including photolithography, wet etching, and anodic bonding. After standard clean and drying, a two-side polished (100) silicon wafer is thermally dry oxidized to form a layer of SiO2, which is used as a hard mask for anisotropic wet etching as illustrated below. Firstly, one side of the silicon wafer is spun coated with a photoresist (PR) (**Figure 4a**). The patterned transfer from a mask onto the wafer is established via exposure and develop‐ ment (**Figure 4b**). Subsequently, buffered oxide etch (BOE) solutions are used to strip off the exposed SiO2 (**Figure 4c**), and the remanent PR is removed by a cleaning step (**Figure 4d**). Then, some micro-grooves with trapezoidal cross sections are created by wet etching (**Figure 4e**). For flow visualization, a Pyrex 7740 glass is finally bonded with the silicon wafer after removing the SiO2 layer using HF solution (**Figure 4f**). Before silicon-to-glass bonding, the laser drill technology is employed to create the inlet/outlet holes for evacuating and charging. After the completion of the MEMS fabrication process, the wafer is sliced into individual dice.

**Figure 4.** Fabrication processes of a MEMS-based MHP: (a) spin coating photoresist, (b) UV exposure, (c) BOE etching (d) wet etching, (e) HF etching silicon layer, and (f) silicon-to-glass anodic bonding.

In addition to the orientation-dependent etching processes, a more elaborate technique was developed that utilizes the multi-source vapor deposition process [31, 32] to create an array of long, narrow channels of triangular cross-section lined with a thin layer of copper. This process begins with the fabrication of a series of square or rectangular grooves in a silicon wafer. Then, the grooves are closed using a dual E-beam vapor deposition process, creating an array of long narrow channels of triangular cross section with two open ends. **Figure 5** gives a SEM image of the end view of a vapor deposited MHP which has not quite been completely closed at the top. Clearly, the MHPs are lined with a thin layer of copper, and thus the migration of the working fluid throughout the semiconductor material could be significantly reduced.

**Figure 5.** A vapor-deposited micro-grooved heat pipe [17].

## **3. State-of-the-art of research on MEMS-based micro-grooved heat pipes**

#### **3.1. Experimental investigation**

The original conception of micro-grooved heat pipes fabricated in silicon substrate was first introduced by Cotter, but the first experimental test results on these micro-devices were not published until somewhat later by Peterson and coworkers [26]. In their investigation, several silicon wafers as shown in **Figure 6** were fabricated with distributed heat sources on one side and an array of MHPs on the other. As an intermediary step in the development process, experimental tests were conducted by Babin et al. [8] on two individual micro-grooved heat pipes, one copper and one silver, approximately 1 mm2 in cross-section area and 57 mm in length. Distilled and deionized water were used as the working fluid.

**Figure 6.** Array of micro-grooved heat pipes fabricated on silicon wafer [26].

After that, Peterson's group carried out several experimental and numerical investigations [28, 31, 33, 34] to verify the feasibility of MHPs as an integral part of semiconductor devices, and then a large number of experimental investigations have been conducted by other researchers to extend the MHP array concept and determine the potential advantages of MEMS-based MHPs.

In 1993, Peterson et al. [28] carried out the experiment on MHP arrays fabricated in silicon chips. As compared to a plain silicon wafer, their experiment demonstrated that the silicon chips of the same size integrated with rectangular and triangular MHP arrays charged with methanol could obtain reductions in the maximum temperature of 14.1 and 24.9°C, respec‐ tively, at a power input of 4 W. The effective thermal conductivities of these two MHP arrays were increased by 31 and 81%, respectively. Due to the higher capillary pumping effect, it is found that the thermal performance of a triangular MHP is better than that of a rectangular one. However, the experimental investigation by Badran et al. [35] shown an indistinctive increase in effective thermal conductivity after using MHP arrays fabricated on silicon substrate. Compared to plain silicon, the effective thermal conductivities were only increased by about 6 and 11% at high power levels using methanol and water as working fluids, respectively, which are far less than the predicted values based on a theoretical model. This result was found to be similar to the experimental results conducted by Berre et al. [36], according to whom that there was only a systematic slight temperature decrease in the charged MHP array of 55 parallel triangular-shaped channels for filling ratios between 6 and 66% as compared with the empty MHP array at a heat input range between 0.5 and 4 W. However, this temperature discrepancy was found to be comparable to the experimental uncertainty and therefore no significant heat transfer enhancement could be clearly identified. These authors believed that it is mainly attributed to the large thermal conductivity of silicon, and therefore, a large part of heat is transferred by conduction through the silicon material and that the improvement due to the MHP array is negligible.

To enhance performance of MHPs, Kang and Huang [37] proposed two silicon MHPs with star and rhombus grooves, as illustrated in **Figures 7**a, b, respectively. The heat transfer performance of these MHPs was improved due to better capillarity provided by more acute angles and micro-gaps. Experimental results demonstrate that for the silicon wafer with an array of 31 star-grooved MHPs (340 μm in hydraulic diameter) filled with 60% methanol at a power input of 20 W, reduction in the maximum wafer temperature was 32°C. For the silicon wafer with an array of 31 rhombus-grooved MHP (55 μm in hydraulic diameter) filled with 80% methanol at a power input of 20 W, reduction in the maximum wafer temperature was 18°C. The best thermal conductivities of star and rhombus grooves MHPs were found to be 277.9 and 289.4 W/(m K), respectively.

Berre et al. [36] fabricated two sets of MHP arrays in silicon wafers. The first array, as illustrated in **Figure 8**a, was made from two silicon wafer with 55 triangular parallel micro-channels (230 μm in width and 170 μm in depth); and the second array, as illustrated in **Figure 8**b, was made from three silicon wafers having two sets of 25 parallel micro-channels, with the larger ones placed on the top of the smaller ones. The smaller triangular channels were used as arteries drain the liquid to the evaporator, so the liquid returns via independently etched channels to the evaporator rather than common liquid–vapor counter-current flow as occurred in **Figure 8**a, and thus significantly reducing the liquid–vapor interactions and enhancing the heat transport limitation. Ethanol and methanol were used as the working fluids. Filling ratios ranging from 0 to 66% were tested. The effective thermal conductivity evaluated by a 3D simulation was found to be 600 W/(m K), which represented an increase of 300% of the silicon thermal conductivity at high heat flux, demonstrating remarkable heat transfer enhancement.

**Figure 7.** Schematic diagram of star grooves MHP (a) and rhombus grooves MHP (b) [37].

**Figure 8.** Transverse cross-sections of a MHP array (a) with triangular channels and (b) with triangular channels cou‐ pled with arteries [36].

Recently, a novel artery MHP array as illustrated in **Figure 9** was proposed by Kang et al. [38] to enhance the liquid backflow. Two smaller channels serving as arteries are positioned on both sides of one vein channel which acts as the ordinary MHP, and these channels are connected together at both ends by two connecting channels. Because of the two ends' pressure difference of the V-shape grooves in the MHP array, the working liquid gathered at the

**Figure 9.** Schematic diagram of the MHP and artery and working principle [38].

condenser could be transported to the evaporator both through the MHPs' grooves and arteries. Soon afterward, the same group [39] stated that implanted arteries can effectively enhance the capillarity thus improving the capability to transport the liquid from the cold end back to the hot end, and limiting the propagation of dry-out region.

In addition to the artery MHPs, micro-grooves with non-parallel cross section were also utilized to enhance capillary effect and then heat transport capability of MHPs by Luo et al. [40]. A silicon-glass MHP with non-parallel micro-channel structure was put forward, having larger dimension of grooves in the evaporator section in comparison with that in the condenser section. Besides, a vapor chamber was wet etched onto the Pyrex 7740 glass and then bonded with the channel-etched silicon wafer as illustrated in **Figure 10**. The depths of the microgrooves and vapor chamber in the silicon wafer and Pyrex 7740 were about 160 and 200 μm, respectively. Experimental results show that the non-parallel micro-channels could enhance the capillarity of liquid back flow from the condenser to the evaporator of the MHP and then improve the thermal performance. Also, it reveals that the vapor chamber influenced the performance of the MHP and a suitable design could reduce the vapor flow resistance and hence enhancing the liquid back flow. The novel MHPs demonstrate 10.6 times higher in the maximum equivalent thermal conductivity than that of the pure silicon wafer.

**Figure 10.** Schematic diagram of a micro-heat pipe with a vapor chamber [40].

In order to comprehensively understand the thermal performance of MHPs, micro-tempera‐ ture sensors including poly-silicon integrated thermistors [36, 41–44] and platinum resistance temperature detectors (RTDs) [45] were used to obtain temperature profile along the longitu‐ dinal axis of a MHP array precisely.

#### **3.2. Theoretical analysis**

While some analytical models that predict the heat transfer limitations and operating charac‐ teristics of individual MHPs have been developed [46–49], it is unclear how the incorporation of an array of these MHPs on a silicon wafer might affect the temperature distribution and the resulting thermal performance. Hence, Mallik et al. [31] developed a three-dimensional numerical model capable of predicting the thermal performance of an array of parallel MHPs constructed as an integral part of semiconductor chips. In order to determine the potential advantages of this concept, several different thermal loading configurations were analyzed. The reduction in maximum chip temperature, localized heat fluxes, and maximum tempera‐ ture gradient across the chip as a function of the number of MHPs in the array was determined. Besides, the 3D numerical model was further extended to determine transient response characteristics of an array of MHPs integrated on silicon wafers. Numerical results show significant reductions in the transient response time, indicating the effectiveness of an array of these MHPs in dissipating heat over the entire chip surface and improving the heat removal capability. The transient thermal response was measured and compared with the calculations based on the numerical model proposed by the same group [33].

Suman and Kumar [50] and Suman and Hoda [51, 52] developed several one-dimensional models, which include the substrate effect, to predict the thermal characteristics of MHPs embedded in a silicon chip. These models are considerable simpler in form and easier to implement than those developed by other, while less accurate since only the fluid phase were took into account and neglected the liquid–vapor interface shear effect.

#### **3.3. Novel designs for performance improvement**

According to the working principles of a MHP, the liquid back flow is derived from a difference in the radius of curvature between the hot part and the cold part. Therefore, its heat transfer capacity is less than that of a conventional heat pipe having wicking structures. Owning to its advantages of simple design and direct integration on the silicon wafers, suitable for many applications, several attempts have been made in the past to increase the transport capability of MHPs.

By applying electric field at the liquid–vapor interface, pressure difference can be increased if the working fluid is dielectric in nature. This research is based on the assumption that both augmentation of the heat transport capability and active thermal control of MHPs can be achieved through the application of a static electric field. Yu et al. [53] conducted experimental and theoretical analyses to evaluate the potential benefits of electrohydrodynamic (EHD) forces on the operation of MHPs. In their experiments, the electric fields were used to orient and guide the flow of the dielectric liquid within the MHP from the condenser to the evapo‐ rator, and then a six time increase in the heat transport capability was obtained. The application of an electric field to MHPs not only can enhance the heat transfer capacity but also permits active thermal control of sources subject to transient heat loads and thus making the temper‐ ature control more precise [54].

Using EHD-assisted MHPs, the substrate temperature can be controlled more precise by varying the field strength. But the model developed by Yu et al. [53, 54] are semi-empirical in nature. The effect of electrical field has not been directly incorporated into flow of fluid. Therefore, a model developed from the first principle and its experimental validation is required to understand the effect of an electrical field in the performance of MHPs. Such an attempt has been presented by Suman [55] that developed a model for the fluid flow and heat transfer in an EHD-assisted MHP considering the coulomb and dielectrophoretic forces. The analytical expressions for the critical heat input and for the dry-out length have been obtained. It was found that the critical heat input could be increased by 100 times using EHD.

To provide enough capillary pressure to collect more working fluid at the evaporator region passively and enlarge the capillary limitation, surface wettability treatment of inner wall along the longitudinal direction of a MHP offers a possible solution. Qu et al. [56] proposed a triangular MHP characterized by a gradient inner surface, with the evaporator, adiabatic section, and condenser having different surface wettabilities and hence contact angles. The contact angle decreases from the condenser to the evaporator, thereby enhancing heat transfer capacity. The results revealed that the surface with a gradient wettability increased the maximum heat input of the MHP up to 49.7%, compared with that of uniform surface wettability. The effect of surface-tension gradient on the thermal performance of a MHP has been numerically investigated by Suman [57]. Results show that the liquid pressure drop across the MHP can be decreased by about 90%, and the maximum heat throughput can be increased by about 20% with a favorable surface-tension gradient. A mixture of water and normal alcohol with carbon chain ranging 4–7 (like water-butanol mixture) was suggested to

**Figure 11.** A radial-grooved micro-heat pipe: vapor-phase grooves (top left); interface (top right); liquid phase grooves (bottom) [58].

use as a liquid solution whose surface tension increases with the increase of temperature. The favorable effects will promote the fluid flow from the cold end to the hot end resulting in the heat transfer enhancement of a MHP.

A radial-grooved MHP as illustrated in **Figure 11** was designed and fabricated in silicon wafer by Kang et al. [58]. This radial-grooved MHP consisted of a three-layer structure, with the middle layer serving as the interface between liquid and vapor phases flowing in the upper and bottom layers, respectively. The separation of the liquid and vapor flow was designed to reduce the viscous shear force. This MHP with a size of 5 cm × 5 cm was fabricated by bulk micro-machining and eutectic bonding techniques. Both the vapor and liquid phase grooves were 23 mm in length and trapezoidal in shape, with 70 grooves spreading in a radial manner from the center outward. For the vapor phase grooves, the widths at the inner and outer ends of the grooves were 350 and 700 μm, respectively. The corresponding widths for the liquid phase grooves at inner and outer end are 150 and 500 μm, respectively. The best heat transfer performance of 27 W at a filling rate of 70% was obtained for this micro-device. Later, Kang et al. [59] presented two wick designs of MHPs with three copper foil layers. The first design has almost the same structures as depicted in **Figure 11** and worked based on the same principle and advantages of liquid–vapor separation, whereas the second one had 100-mesh copper screens as wicking structure (**Figure 12**). It was found that the radial grooved MHP, filled with methanol at a filling ratio of 82%, showed better performance at a heat input of 35 W than that using mesh screens as wicking structure.

**Figure 12.** The diagram about the structures of each layer of a copper-screen-styled micro-heat pipe heat spreader: gas phase (left); partition panel (central); liquid phase (right) [59].

## **4. Other emerging MEMS-based MHPs**

In addition to MEMS-based micro-grooved heat pipes, some other mini- or micro-scale heat pipes, such as capillary pumped loops (CPLs) [60–64], loop heat pipes (LHPs) [65–69], oscillating heat pipes (OHPs) [70–75], and vapor chambers (VCs) [76–80] as shown **Figure 13**, were also successfully constructed on silicon substrates by means of micro-fabrication technique recent years and became two-phase passive micro-coolers for electronic cooling.

**Figure 13.** Novel MEMS-based micro-heat pipes: (a) micro-CPL [62], (b) micro-LHP [65], (c) micro-OHP [72], and (d) micro-vapor chamber [77].

Similar to MEMS-based micro-grooved heat pipes, these novel MEMS-based MHPs could be considered as small versions of corresponding conventional prototypes and work at the related mechanism. Although some of these micro-devices have more complicated structures in comparison with micro-grooved heat pipes, especially the micro-CPLs and micro-LHP consisting of additional wicking structures, the heat cooling capability is much higher and the maximum allowable heat fluxes could be up to 185.2 W/cm2 [63] and 300 W/cm2 [68] for micro-CPLs and micro-LHP, respectively.

In addition to MEMS-based loop-type heat pipes as shown in Figure 13a–c, MEMS-based VCs are also utilized for spreading high local heat flux and act as silicon heat spreaders. A silicon VC illustrated in **Figure 13**d based on a unique three-layer silicon wafer-stacking fabrication process demonstrated an maximum effective thermal conductivity about 2700 W/(m K) [77], indicating excellent performance to attain temperature uniformity.

To further increase the heat transport capability of micro-VCs, recently micro-/nano-hierarch‐ ical wicking structures are proposed by researches. The materials of carbon nanotube, Ti, and Cu as shown in Figure 14 are available due to the easy-fabrication feasibility and material compatibility. As compared to the micro-wicking structures, the micro-/nano-biwick structure shows better wettability [82, 83] and can sustain ultra-high localized heat flux over 700 W/cm2 [81].

**Figure 14.** SEM images of micro-/nano-hierarchical wicking structures for micro-vapor chamber: (a) biwick structure composed of cylindrical CNT pillars [81]; (b) biwick structure composed of straight CNT stripes [81]; (c) Ti pillar array with oxidized hairlike NST(nanostructured titania) [82]; (d) nanostructured Cu micro-posts [83].

## **5. Applications of MEMS-based MHPs**

The most ongoing and potential application of MEMS-based MHPs is in the thermal manage‐ ment of electronics [84, 85]. Adkins et al. [86] discussed the use of a "heat-pipe heat spreader" embedded in a silicon substrate as an alternative to the conductive cooling of integrated circuits using diamond films. These MHPs function as highly efficient heat spreaders, collecting heat from the localized hot spots and dissipating the heat over the entire chip surface. Incorporation of these MHPs as an integral part of silicon wafers has been shown to significantly reduce the maximum wafer temperature and reduce the temperature gradients occurring across these devices [28, 32]. Currently, mobile electronics, such as smart phones and tablet PCs, are widely used and becoming an alternate solution of traditional PCs or notebooks. These devices comprise many high-heat-generating components and have been miniaturized and designed for high-density packaging. The complex thermal behavior due to their usage under various circumstances affects the reliability and usability. The ultra-compact cooling space demands of these mobile electronics make the MEMS-based MHPs a good alternative solution as compared to other cooling schemes.

The biological field associated with human disease remedy is another potential application of MEMS-based MHPs. MHPs can provide a controllable heat rate at constant temperature and may be matched to the thermal conductivity of live tissue and the degree to which a cancerous tumor is perfused. They may be useful in treating cancerous tumors in body regions that cannot be treated by other means [87, 88].

In addition to the above applications, the thermal management of localized heat generating devices such as concentrated solar cells, MEMS-based infrared detectors and micro-fuel cells as well as thermal energy harvesting devices is also possible fields that MEMS-based MHPs can be used.

## **6. Summary**

In this chapter, a generalized concept of MEMS-based MHPs is proposed on the basis of the initial description of MHP by Cotter as an integral part of semiconductor devices. The working principle, capillary limitation, fabrication process as well as the state-of-the-art of MEMS-based micro-grooved heat pipes have been introduced firstly and discussed in detail. Some new MEMS-based MHPs, including micro-CPLs, micro-LHPs, micro-OHPs, and micro-VCs, and some of their structures and thermal characteristics have been presented. In view of the continued trend in miniaturization of electronic/optoelectronic devices and circuits and explosive growth of MEMS products, MEMS-based MHPs exhibit advantages and will find increasing applications in related engineering and medical fields. More research work is needed to provide rational tools for optimal designs and fabrications of these micro-devices.

#### **Acknowledgements**

This work was supported by the National Natural Science Foundation of China (Nos. 51206065 and 51576091) and China Postdoctoral Science Special Foundation (No. 2015T80523).



## **Author details**

Qu Jian\* and Wang Qian

\*Address all correspondence to: rjqu@mail.ujs.edu.cn

School of Energy and Power Engineering, Jiangsu University, Zhenjiang, China

## **References**


#### MEMS-Based Micro-heat Pipes http://dx.doi.org/10.5772/62786 103
